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Robust Control for a Class of T-S Fuzzy Systems with Interval Time-varying Delay

Shengtao Li, Yuanwei Jing, and Xiaomei Liu
International Journal of Control, Automation, and Systems, vol. 10, no. 4, pp.737-743, 2012

Abstract : The problem of delay-dependent stability analysis and controller design for a class of T-S fuzzy systems with interval state time-varying delay is considered. Based on Lyapunov stability theory, defining a new Lyapunov-Krasovskii functional and introducing some free-weighting matrices, a new delay-dependent criterion is given to ensure the systems asymptotically stable. The merit of the pro-posed conditions lies in the less conservativeness than the existing ones, which is achieved by consid-ering the mean of time-delay interval and the introduction of the free variables. By the concept of par-allel distributed compensation (PDC), a delay-dependent condition for the existence of a fuzzy state feedback control law with memory is proposed. Another merit is the consideration of the memory of the controller. All conditions are shown in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using the LMI optimization techniques. Two numerical examples are given to il-lustrate the feasibility and validity of the proposed approach.

Keyword : Interval time-varying delay, linear matrix inequality (LMI), Lyapunov-Krasovskii functional, T-S fuzzy systems.

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